I know star san's surficants will eventually come out of solution and leave a white gunky film... potentially clogging up the plate chiller's passage ways. I do not know the effects of PBW's surfficants, however, being an oxidative cleaner, I suspect extremely long term contact with stainless is not adviseable. While stainless is resistant to oxidation, it is not 100% impervious to it, and if you leave it in contact with an oxidative cleaner "forever" my guess is that you will see negative effects in the long run.
Also, if the inner workings of the plate chiller are aluminium or copper, then PBW is really not good for long term contact.